In training a neural network, must you include a bias?

Question

I'm actually working on answering this question (from an examination):

Show in tabular form the first five epochs of the training of a perceptron to perform the Boolean OR operation; using initial weights of 0.3 and -0.2; a threshold value of 0.2; and the learning rate of 0.1

I've produced an answer here: https://docs.google.com/spreadsheet/pub?key=0AqDm6Izoam4OdF9sWXNQT0FqOF90UWpTeC1LdTd4VUE&output=html

But unlike the example in Wikipedia, I haven't included a bias. Is it necessary?

Looking at this answer http://stackoverflow.com/questions/2480650/role-of-bias-in-neural-networks, no, I don't think you HAVE to have it — Daniel, May 16 '13 at 15:11
@FranckDernoncourt, "Inputs: x0, x1, x2, with input x0 held constant at 1." — Irwin, May 16 '13 at 15:25

score 1 · Accepted Answer · edited May 23 '17 at 12:13

No, you don't need to have a bias node in your neural network - many networks can still converge to a solution without one. However, given that neural network convergence can sometimes be finicky, having a bias node is generally a good idea. Essentially, as discussed here Role of Bias in Neural Networks, it gives the neural net a way to adjust how high an activation level needs to be in order for a node to fire. It's kind of conceptually similar to including a y-intercept in a line equation.

In training a neural network, must you include a bias?

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